According to the observation in experiment of stability of the oil film, the assumption of velocity distribution for both the water flow and the oil film is introduced. On the basis of the assumption, Orr-Sommerfeld s...According to the observation in experiment of stability of the oil film, the assumption of velocity distribution for both the water flow and the oil film is introduced. On the basis of the assumption, Orr-Sommerfeld stability equation is applied to develop the method of determining the critical velocity of the oil film, and the criterion for stability of the oil film is obtained. Meanwhile, a formula describing the relation between the thickness of the oil film and the velocity of the water flow is also given and examined by the laboratory experiment.展开更多
Nonlinear methods are combined with Runge Kutta methods to develop A stable explicit nonlinear Runge Kutta methods for solving stiff differential equations and a class of the third order formulae are constructed.I...Nonlinear methods are combined with Runge Kutta methods to develop A stable explicit nonlinear Runge Kutta methods for solving stiff differential equations and a class of the third order formulae are constructed.It avoids solving the nonlinear equations which implicit methods must solve. Implementation is very simple and the computation cost for each step is small.This paper uses a shift transformation to avoid the order reduction of nonlinear methods at y = 0 . Thus the method is very practicable. Numerical tests show that the method is more efficient than explicit methods or implicit methods of the same order.展开更多
文摘According to the observation in experiment of stability of the oil film, the assumption of velocity distribution for both the water flow and the oil film is introduced. On the basis of the assumption, Orr-Sommerfeld stability equation is applied to develop the method of determining the critical velocity of the oil film, and the criterion for stability of the oil film is obtained. Meanwhile, a formula describing the relation between the thickness of the oil film and the velocity of the water flow is also given and examined by the laboratory experiment.
基金Supported by the National Natural Science Foundationof China(No.195 710 4 6 )
文摘Nonlinear methods are combined with Runge Kutta methods to develop A stable explicit nonlinear Runge Kutta methods for solving stiff differential equations and a class of the third order formulae are constructed.It avoids solving the nonlinear equations which implicit methods must solve. Implementation is very simple and the computation cost for each step is small.This paper uses a shift transformation to avoid the order reduction of nonlinear methods at y = 0 . Thus the method is very practicable. Numerical tests show that the method is more efficient than explicit methods or implicit methods of the same order.
